We derive a supersymmetric renormalization group (RG) equation for the scale-dependent superpotential of the supersymmetric OðNÞ model in three dimensions. For a supersymmetric optimized regulator function, we solve the RG equation for the superpotential exactly in the large-N limit. The fixed-point solutions are classified by an exactly marginal coupling. In the weakly coupled regime there exists a unique fixed-point solution, for intermediate couplings we find two separate fixed-point solutions and in the strong coupling regime no globally defined fixed-point potentials exist. We determine the exact critical exponents both for the superpotential and the associated scalar potential. Finally, we relate the hightemperature limit of the four-dimensional theory to the Wilson-Fisher fixed point of the purely scalar theory.
We study the supersymmetric N = (2, 2) Wess-Zumino model in two dimensions with the functional renormalization group. At leading order in the supercovariant derivative expansion we recover the nonrenormalization theorem which states that the superpotential has no running couplings. Beyond leading order the renormalization of the bare mass is caused by a momentum-dependent wave function renormalization. To deal with the partial differential equations we have developed a numerical toolbox called FlowPy. For weak couplings the quantum corrections to the bare mass found in lattice simulations are reproduced with high accuracy. But in the regime with intermediate couplings higher-order-operators that are not constrained by the nonrenormalization theorem yield the dominating contribution to the renormalized mass.
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